Question 923800
{{{x(x+1)(x+2)=720}}}
{{{x(x^2+3x+2)=720}}}
{{{x^3+3x^2+2x-720=0}}}


Use synthetic division for Rational Roots Theorem and examine only the positive possible roots.  You are also only interested in the possible roots less than 180 (just a guess).


I found only this:


_______8______|_______1______3_______2_______-720
______________|
______________|
______________|_____________8_______88_______720
______________|________________________________________
_____________________1______11_______90________0



One of the binomial factors is {{{highlight(x-8)}}} for a root of 8.  This is the only rational root found  (used a graph to check).


Your three whole numbers are 8, 9, 10.